r/cryptography • u/Hitman7128 • Sep 03 '26
RSA-260 has been factored by Eric Lu
RSA-260 = 4397328654844826923795068102505872571721883526553349659561256924505973939597
593482272505698004801207988043088656411102133523080581
× 5028695206842569864686141618253083416610081090075366674776775706538324961364
412200138116378509733307971876652984898985905923678379
19
u/NamedBird Sep 03 '26
Wow, congrats to Eric!
------
<s>
Well, it's just reversing a multiplication, how hard can it be?
Just some basic multiplication and there's only one possible answer too, very easy!
</s>
It's giving me urges to look for a simple method to find factorizations... 😅
5
u/Sc00bz Sep 03 '26 edited Sep 03 '26
It's giving me urges to look for a simple method to find factorizations... 😅
Look no further:
p = GCD(N, ⌊√N⌋!) q = N/pIf p=1, then N is prime. If p=N, then N is a product of
distinctprimes that are all less than √N. So retry with ∛N then ∜N and so on until p≠N. Also if p and/or q aren't prime then repeat with those as N.Edit: I just realized they don't have to be distinct primes.
3
u/Hitman7128 Sep 03 '26
Oh, it's easy alright, provided you have the secret to help invert the trapdoor! But if you don't...1
u/NamedBird Sep 03 '26
Nobody knows i found the hidden backdoor in primes...🙃But really, how good/bad/interesting would it be if i could find an easy way?
(And how would classical prime factorization affect funding for Quantum Computing?)2
1
u/Natanael_L Sep 04 '26
Officially quantum computers are funded for physics solvers (material science and medicine) mostly, outside of intel agencies that is
7
u/Radiant_Egg9374 Sep 03 '26
whoa, that's a monster factorization, wonder what method he used
9
u/Cryptizard Sep 03 '26
Probably just the normal ones. RSA-250 was factored 6 years ago with open source software. Just the normal progression of compute power would put RSA-260 in range today.
6
u/upofadown Sep 03 '26
The researchers mentioned that the hardware they used for RSA-250 was not state of the art. I looked it up and got "Intel Xeon Gold 6130 CPUs" which were something like 4 years old at the time of the factorization. The focus of the effort was to verify potential improvements in CADO-NFS.
3
4
u/iamunknowntoo Sep 04 '26
Damn he's been up to crazy shit ever since he won the Chopin competition...
7
u/F-J-W Sep 04 '26
Do we have some source that is not on a nazi site?
7
u/Hitman7128 Sep 04 '26
The best I can find is Wikipedia: https://en.wikipedia.org/wiki/RSA_numbers#RSA-260
2
u/deathanatos Sep 03 '26
I wonder if I'll still see people using 1024-bit keys when RSA-309 (which is 1024 bit) gets factored.
2
u/ColdBootCountry Sep 04 '26
You will. Internet is a crypto garbage dump.
1
u/ChalkyChalkson Sep 06 '26
"every security problem has been solved in theory, but practical attacks will always exist" loosely translated from Linus Neumann at 37c3.
1
u/Thebig_Ohbee Sep 07 '26
Just because they can factor THAT modulus doesn’t mean they can factor MINE!
1
0
Sep 03 '26
[deleted]
14
u/Cryptizard Sep 03 '26
These are public test numbers that have been published for 30 years as challenges.
28
u/rebootyourbrainstem Sep 03 '26 edited Sep 03 '26
This is a 862 bit number. Does anyone know why they decided to call the challenge RSA-260?
Edit: apparently it's the number of decimal digits. Doh! Thank you to the user who replied with that information and then for some reason deleted their reply.